The cat in the box has a 50% change of dying and a 50% chance of being alive. Making the assumption that when the box is closed you can't tell if the cat is alive, the cat can be considered to both be alive and dead, in a 50/50 probability.
Now your lotto ticket in your wallet is the same, except the odds are different. There is a 1 in a 100 million (or some other similar large number) chance that your lotto ticket is the winner. There also is the inverse of that chance that your lotto ticket is NOT the winner. As long as you don't scratch the ticket, or look at the winning lotto numbers, it still has that slight chance. Both a minimally winning ticket and an almost guaranteed losing ticket. The main difference here is that the "one in a million" only matters if you have all the tickets. For the purposes of an argument, it is more applicable than a cat because numbers don't die from lack of air and starvation after a few weeks locked in a box.
No the odds wouldn't change the longer you wait to look (unlike a cat in a box). The percentages are still the same. If everyone shredded their lotto ticket except you, then the odds would change. But that isn't likely to happen.
Some theories of parallel dimensions (at least in sci fi for sure anyways) say that any slight change in this universe causes another universe to be made.
So the 1 in 100 million universes that are made when you buy that lotto ticket will win. The 99,999,999 others will have lost.
That is if that theory is correct, which we don't know, and it doesn't seem too likely.
But what do I know?